I am looking to install a claw foot bathtub. Right now there is only a shower and sink. I can tie into either of these drains and supply lines but the sink is more convenient. The sink drain is 1.5". Will that work? Do I need a p-trap on the tub? Are there any potential problems? The sink is only about 3 feet from where the tub plumbing will be and the shower is about 7 feet. Thank you for your help!